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V= ε X V (x, y) χΩ (x) χΩ (y) a*(x) a*(y) a (y) a (x) of the ideal Fermi-gas on the lattice Έv, where Ωis a finite subset ofTΠand χΩ is its indicator. The invertibility of Moller morphisms for small ε is proven. It follows that in the cyclic GNS representation with respect to KMS states the dynamics of ideal and locally perturbed Fermi-gas are unitary equivalent.